Robust Multivariate Detection and Estimation with Fault Frequency Content Information

TL;DR

This paper develops a robust framework for fault detection and estimation in LTI systems that leverages frequency content information, optimizing detection filters and estimation strategies under noise and disturbance constraints.

Contribution

It introduces a novel optimization approach for frequency-specific fault detection and estimation, including a tractable lower bound and an alternating optimization method for non-convex problems.

Findings

Validated on hydraulic turbine and power system models.

Achieved improved fault sensitivity in targeted frequency ranges.

Demonstrated effectiveness in reducing false alarms and detection delays.

Abstract

This paper studies the problem of fault detection and estimation (FDE) for linear time-invariant (LTI) systems with a particular focus on frequency content information of faults, possibly as multiple disjoint continuum ranges, and under both disturbances and stochastic noise. To ensure the worst-case fault sensitivity in the considered frequency ranges and mitigate the effects of disturbances and noise, an optimization framework incorporating a mixed H_/H2 performance index is developed to compute the optimal detection filter. Moreover, a thresholding rule is proposed to guarantee both the false alarm rate (FAR) and the fault detection rate (FDR). Next, shifting attention to fault estimation in specific frequency ranges, an exact reformulation of the optimal estimation filter design using the restricted Hinf performance index is derived, which is inherently non-convex. However, focusing on finite frequency samples and fixed poles, a lower bound is established via a highly tractable quadratic programming (QP) problem. This lower bound together with an alternating optimization (AO) approach to the original estimation problem leads to a suboptimality gap for the overall estimation filter design. The effectiveness of the proposed approaches is validated through applications of a non-minimum phase hydraulic turbine system and a multi-area power system.